{"paper":{"title":"Critical Phase of Bond Percolations on Growing Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Koji Nemoto, Takehisa Hasegawa","submitted_at":"2010-04-06T08:28:02Z","abstract_excerpt":"The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^\\psi$ and the mean number of clusters with size $s$ per node follows a power function $n_s \\propto s^{-\\tau}$ in the whole range of open bond probability $p$. The exponent $\\tau$ and the fractal exponent $\\psi$ are also derived as a function of $p$ and the degree exponent $\\gamma$, and are found to satisfy the scaling relation $\\tau=1+\\psi^{-1}$. Numerical results with several network sizes are quite well fitted by a finite size scaling for a wid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0795","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}